A151428 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (-1, 0), (0, -1), (1, -1), (1, 1)}.

1, 0, 2, 2, 10, 22, 90, 236, 970, 2952, 11436, 39148, 148540, 536112, 2051152, 7635144, 29434148, 112247828, 436062188, 1690577540, 6627115320, 25997584500, 102759869944, 406976897928, 1620332871368, 6467542523728, 25916980121976, 104121128124540, 419635266596960, 1695299659717500

Offset

0,3

Links

Table of n, a(n) for n=0..29.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

Mathematica

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A336490 A230893 A151389 * A341680 A213338 A309753

Adjacent sequences: A151425 A151426 A151427 * A151429 A151430 A151431

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved